# Voltage across an inductor after flipping a switch

• Eitan Levy
In summary: The energy is still there when the switch is closed, it is just being used in the circuit. I don’t believe that this is possible. The energy is still there when the switch is closed, it is just being used in the circuit.
Eitan Levy
Homework Statement
In the circuit below the initial charge of the capacitor is Q. First, we shut S1 (S2 remains open) and wait for the first time in which the energy of the capacitor is minimal.
Then, we shut S2 and open S1 simultaneously. What is the voltage on the inductor right after the change?
Relevant Equations
ω=1/sqrt(LC)
I(t)=-ωQsin(ωt)
When the energy of the capacitor is minimal it has no charge therefore the voltage on it is 0. That means that the voltage on the inductor is 0 as well at the moment.
The part that confuses me is: why isn't the correct answer 0? How can a voltage change in a single moment?
Furthermore I am confused because in the solution, they used the fact that the current in the inductor before the change was Q/sqrt(LC) and therefore got the answer QR/sqrt(LC) . Why can the voltage shift like that but the current can not? How can we know what will remain constant (for a moment, in this case the current), and what may change instantly?

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It's ok for voltage and current to change suddenly in a circuit. A simple example is a circuit with a battery, switch and resistor. When the switch is closed, there is suddenly a voltage across the resistor and a current through the resistor. (Every circuit is going to have some inductance which prevents the current from changing truly instantaneously. But, if the inductance is very small, the current can change essentially instantaneously.)

At the moment the switching occurs in your circuit, is there any energy in the circuit? Can the energy change suddenly?

TSny said:
It's ok for voltage and current to change suddenly in a circuit. A simple example is a circuit with a battery, switch and resistor. When the switch is closed, there is suddenly a voltage across the resistor and a current through the resistor. (Every circuit is going to have some inductance which prevents the current from changing truly instantaneously. But, if the inductance is very small, the current can change essentially instantaneously.)

At the moment the switching occurs in your circuit, is there any energy in the circuit? Can the energy change suddenly?
I figured it will have something to do with energy. As far as I know energy cannot change instantly. The energy is 0.5LI^2, therefore I cannot change suddenly?

Eitan Levy said:
I figured it will have something to do with energy. As far as I know energy cannot change instantly. The energy is 0.5LI^2, therefore I cannot change suddenly?
Yes. Just before the switching, the inductor has the energy ##\frac 1 2 L I^2##. This energy must still be in the LR circuit after the switching (unless the energy was dissipated in sparking in the switches, which we assume doesn't happen.)

TSny said:
Yes. Just before the switching, the inductor has the energy ##\frac 1 2 L I^2##. This energy must still be in the LR circuit after the switching (unless the energy was dissipated in sparking in the switches, which we assume doesn't happen.)

One question about this - does the energy must be continuous in the entire circuit or in the inductor itself? Can the energy completely "disappear" from the inductor instantly, while moving somewhere else?

Eitan Levy said:
Can the energy completely "disappear" from the inductor instantly, while moving somewhere else?
I don’t believe that this is possible.

Eitan Levy

## 1. What happens to the voltage across an inductor after flipping a switch?

After flipping a switch, the voltage across an inductor will initially spike to its maximum value, then gradually decrease over time.

## 2. Why does the voltage across an inductor spike after flipping a switch?

This spike in voltage is caused by the sudden change in current flow through the inductor. According to Faraday's law of induction, a change in magnetic field induces a voltage in a conductor, which results in the spike.

## 3. How long does it take for the voltage across an inductor to reach its maximum value after flipping a switch?

The time it takes for the voltage across an inductor to reach its maximum value depends on the inductance of the inductor and the resistance of the circuit. Generally, it takes a few milliseconds for the voltage to reach its maximum value.

## 4. What happens to the voltage across an inductor if the switch is flipped multiple times?

If the switch is flipped multiple times, the voltage across the inductor will continue to spike and decay accordingly with each switch flip. However, the maximum voltage reached will decrease with each subsequent switch flip due to the inductor's internal resistance.

## 5. Can the voltage across an inductor be controlled after flipping a switch?

Yes, the voltage across an inductor can be controlled by changing the inductance or resistance in the circuit. For example, adding a resistor in series with the inductor can decrease the maximum voltage reached after flipping a switch.

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